We illustrate the sensitivities of LEP experiments to leptonic signals
associated to models where supersymmetry (SUSY) is realized with spon
taneous breaking of R-parity. We focus on missing transverse momentum
plus acoplanar muon events (p(T)' + mu(+) mu(-)) arising from lightest
neutralino single production chi nu as well as pair production chi ch
i, followed by chi decays, where chi denotes the lightest neutralino.
We show that the integrated luminosity achieved at LEP already starts
probing the basic parameters of the theory. We discuss the significanc
e of these constraints for the simplest spontaneous R-parity breaking
models and their relevance for future searches of SUSY particles.